Transferring digital data over a medium is performed using a modulation/demodulation scheme. A discrete multitone modulation method is commonly used in DSL. In DMT modulation, the transferred bits are divided between each one of the discrete tones in such a way to achieve maximum transmit rate with minimum Bit Error Rate (BER). Estimation of the signal to noise ratio (SNR) for each discrete tone is essential to determine how many bits will be assigned to each tone to achieve the desired BER.
U.S. patent application Ser. No. 10/739,388, assigned to the same assignee as the present application, describes a method to estimate the signal to noise ratio that is used in ADSL link. To determine the signal to noise ratio in the channel, the transmit side transmits a known signal—a reverb signal using a 4QAM (quadratic Amplitude Modulation) modulation. 4QAM constellation has four constellation points, each representing two bits of information. The reverb signal is a fixed pseudo random sequence with equal probability to each of the four constellation points—P1, P2, P3 and P4. The power of the transmitted signal is a constant. The receiver determines the power of the noise process by analyzing the distance of the received data values from the constellation points.
FIG. 1 illustrates the constellation domain in the receiver. In FIG. 1, the location of constellation point P1 is (1,1), the location of constellation point P2 is (−1,1), the location of constellation point P3 is (−1, −1) and the location of constellation point P4 is (1, −1). A typical method of estimating the noise power is as follows: First, an acceptance square 10 is defined by the points (2,2), (−2,2), (−2,−2) and (2,−2). If the received data is in the acceptance square 10, the hardware calculates the distance between the data and the nearest constellation point (i.e., P1, P2, P3 or P4), the distance is squared, and the resulting value is accumulated (i.e., summed) for N symbols. If the data is outside of the acceptance square (i.e., in area 12 in FIG. 1), the data is marked as an erasure and is ignored by the algorithm. An average is taken over a large number of samples to get the average noise power and to determine the signal to noise ratio.
The signal to noise ratio is typically calculated using the following method: First, it is observed that for 4QAM the power of the signal is exactly 2. The noise power is calculated as:NP=ΣD(n)2/N Where N is the number of samples that fall within the acceptance square and D(n) is the distance between the n'th sample and the nearest constellation point.
It is well observed that the above method is efficient in high signal to noise ratio, but is not accurate when the signal to noise ratio is low. The reason is two fold: First, the computation ignores the samples that fall outside of the acceptance square even though these samples carry the biggest errors; second, if the error is large enough such as a sample that corresponds to a constellation point which is farther than the closest constellation point, the implementation will underestimate the error.